But COLLADA 1.5 says:
The camera is defined such that the local +X axis is to the right, the lens looks towards the local -Z axis, and the top of the camera is aligned with the local +Y axis (also see the <lookat> element). This orientation is affected by the <asset> element’s <up_axis> value.

I’m confused a bit, camera element has it’s own asset element and there is a global <asset> too.
Does camera element/orientation inherit the global (document) or any parent <asset><up_axis> if <camera> doesnt have one?

The orientation of nested assets overrides those of the parent. They are not in terms of the parent’s parameters. This is covered first thing in <asset> section of the 1.5 PDF specification. That’s the first place you should look for semantics.

Details
In the case of hierarchical <asset> elements, where both the parent and child assets supply a value for the same metadata, such as for <unit>, the child asset’s value supersedes the parent’s value within the scope of the child element. This applies recursively.